Variable denisty in the contiuity and momentum equaiton

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SUMMARY

The discussion focuses on implementing variable density in the continuity and momentum equations for fluid flow with low incompressibility. The key takeaway is the necessity of incorporating equations of state, specifically the ideal gas law represented as P = ρRT, where ρ denotes density. This integration leads to coupled momentum and energy equations, complicating the solution process due to the interdependence of velocity and density as unknowns.

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  • Knowledge of equations of state, particularly the ideal gas law
  • Basic proficiency in numerical methods for solving differential equations
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Fluid dynamics engineers, computational fluid dynamics (CFD) practitioners, and researchers working on variable density flow problems will benefit from this discussion.

hoomanya
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Hi,

I am writing a code for a flow with a low degree of in-compressibility. So in my continuity and momentum equations, the density varies. I have never worked with variable density before so I was wondering, how does one usually decide on how the density varies and go on about solving these equations where you have velocity and density as unknowns in the continuity equations.

I would appreciate any hints.

Thanks,

H
 
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You have to include equations of state.

Such as P=rho*R*T
rho = density

Then your momentum and energy equations are no longer uncoupled.
 

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